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EE-420 Lab 1

Andrew Buchanan

spring 2019

For this first lab simulate, and verify the simulation results with experimental measurements, the circuits seen in Figs. 1.21, 1.22, and 1.24 (use a 1 uF cap in place of the 1 pF cap) of the book. Your results should be similar to, but more complete than, the simulation results seen on pages 17 - 23. In your report, and for each circuit, show the

Circuit schematic showing values and simulation parameters (snip the image from LTspice).
Hand calculations to detail the circuit's operation.
Simulation results using LTspice verifying hand calculations.
Scope waveforms verifying simulation results and hand calculations.
Comments on any differences or further potential testing that may be useful (don't just give the results, discuss them).

Circuit 1 Experiment 1
This is the circuit from fig 1.21 in the book. It is an RC circuit with a voltage source of 1V at 200Hz with a 1x10^-6F capacitor and a 1x10^3ohms resistor

Using the formula for gain from the book

and taking the magnitude of the gain (Vout/Vin)

I calculated the gain to be 0.6227. The angle of the gain is hand calculated with

the angle is hand calculated to be -0.898 radians or -51.5 degrees. To calculate the time delay the formula shown below is used.

This gave us a time delay of 715.1x10^-6 seconds.

From the simulation Vout laggs Vin with a voltage of 0.623V and a time delay of 713.6x10^-6 seconds which matches our hand calculations.

The blue wave is the input to the with a measurment of 1.07V at the peak, and the yellow wave is the measurment of the output at 0.640V. these results

match the hand calculations and simulations. They are slightly different in the experimental results because there is always a little error between simulated and
measured values.

Circuit 2 Experiment 2

This is the circuit from fig 1.22 in the book. It is an RC circuit with a voltage source of 1V at 200Hz with a 2x10^-6F capacitor in parallel with a 1x10^3ohms resistor in series with a 1x10^-6F capacitor

Using the formula from the book we can calculate the parralel impedence.

calculating Vout/Vin inputing Z from the equation above

then i calculated the magnitude of the gain

the hand calculated magnitude of the gain is 0.6935 the angle of the gain is calculated with

the angle is calculated to be -0.119 radians or -6.841 degrees. this angle can be used to solve for the time delay with this equation

this gave us a calculated time delay of-95x10^-6 seconds.

From the simulation Vout laggs Vin with a voltage of .7033V and a time delay of 94.57x10^-6 seconds which matches our hand calculations. which matches

the hand calculations.

The blue wave is the input to the with a measurment of 1.09V at the peak, and the yellow wave is the measurment of the output at 0.740V. these results

match the hand calculations and simulations. They are slightly different in the experimental results because there is always a little error between simulated and
measured values.

Circuit 3 Experiment 3

This is the circuit from fig 1.21 in the book. Figure 1.23 is the same as fig 1.21, but looked at with AC analysis

If I use AC analysis and look at the wave form where it is 200Hz it shows a magnitude of 0.622677 or -4.1147db and an angle of -51.023 degrees which matches our results from the first experiment.

To check the simulated bode plot I used measurments of the circuit at different frequencies to make a bode plot of my own in the table below.

Frequency	10Hz	100Hz	1kHz	10kHz	100kHz	1MHz
Vout/Vin (Gain) simulated	0.998032	0.846733	0.157177	0.0159135	0.00159155	0.000159155
Vout/Vin (Gain) measured	1	0.83	.166	0.0212	0.016	0.0064
db	0dbdb	-1.618db	-15.60db	-33.47db	-35.917db	-43.8764db

Based on the table you can see that my results are very acurate and match my hand calculations and my simulations.

Circuit 4 Experiment 4

This is the circuit from fig 1.24 in the book. It is the same as fig 1.21, but it has a pulse wave input.

we can find the time delay with this equation

which is 700x10^-6 seconds. We can also find the rise time with this equation.

which is 2.2x10^-3 seconds we can verify this with LTspice

In my simulation you can see the time delay and the rise delay

In my measurment you can see my td and tr

	td	tr
theoretical	700us	2.2ms
simulated	709.3us	2.208us
experimental	700us	2.200ms

Conclusion
The experiments in this lab were to review RC circuits, and simulate them with LTspice in multiple ways. It is important to know how to use the values we obtain. Experimental, simulation, and theoretical methods help to understand and assess a problem or experiment with accuracy and precision.

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